Given equation of line is 3x+5y=k...(i) comparing Eq. (i) with lx+my+n=0, we getI=3,m=5 and n=−k Equation of ellipse is 16x2+25y2=400...(ii) On divide Eq (ii) by 400, we get
16x2
400
+
25y2
400
=
400
400
⇒
x2
25
+
y2
16
=1 By comparing with standard form of ellipse
x2
a2
+
y2
b2
=1 we get a=5,b=4 ∵ Condition of tangent n2=a2l2+b2m2 (−k2)=(5)2(3)2+(4)2(5)2 ⇒k2=225+400 ⇒k2=625 ⇒K=±25